Game Theory and the Kyoto Protocol

I thought I'd take a break from depressing news about the financial markets and tackle depressing news about the environment. I just read an article in the Economics Focus section of The Economist: Playing games with the planet, Sep 27, 2007. In that article, The Economist discusses research that analyzes the current impasse over the Kyoto Protocol from the perspective of Game Theory.

Basically, the Kyoto Protocol resembles the Prisoner's Dilemma -- a game where players should cooperate from the perspective of globally optimal payoffs, but the players have incentives that would cause them to defect from cooperation and lead to mutually harmful payoffs. The Prisoner's Dilemma can be ameliorated by converting it from its static form to a repeated game. In the repeated Prisoner's Dilemma, players can see what the other players did during previous rounds and 'punish' them for defection.

As Robert Axelrod (an American political scientist -- who took the science part seriously) and others have demonstrated, the best strategy that emerges for repeated PDs is the so-called 'tit-for-tat' strategy. In most cases, that strategy recommends that (a) players should start by cooperating, (b) if some subset of players defect, then they should be punished by the cooperating players but that this punishment should last no more than the time or magnitude required to get players back in line, and (c) hopefully, all players will return to cooperation.

Michael Liebreich, of New Energy Finance, argues that -- while the current impasse over Kyoto seems to be more like the static PD -- the situation should be seen as being more like the repeated PD. Mr. Liebreich offers hope that, with some alterations to the Kyoto and post-Kyoto attempts to control global warming, something akin to 'tit-for-tat' can bring about a global regulatory mechanism to combat global warming.

Although I admire Mr. Liebreich's no doubt good intentions, I think he is being too optimistic. The flaw with his thinking is that there is another framework to consider beyond Game Theory: externalities. As The Economist cheekily points out:

At any given summit on climate change, it is never long before some politician declares how “urgent” or “vital” or “imperative” it is to stop the planet from overheating. And yet few governments are willing to tackle the problem by themselves. In practice, what these impassioned speakers usually mean is that it is urgent—no, vital!—no, imperative!—for all countries but their own to get to grips with climate change.

This quote nicely sums up the problem with economic externalities (aka, external costs and benefits): The benefits of controlling global warming would be shared with countries not cooperating, but the costs will be borne only by those who cooperate. In other words, countries like the U.S. that refuse to cooperate with global warming treaties will free-ride off the countries that are doing something about global warming.

The logic of repeated PD and 'tit-for-tat' rests on the fact that, in those idealized scenarios, players can monitor defection and can adequately punish defectors. But with externalities, it would be difficult to monitor who benefits even though they are free-riding, and it would be even more difficult to punish free-riders without causing serious lasting damage to both the cooperators and defectors.

For example, let's say Denmark decides to punish America for not cooperating on Kyoto or Kyoto-like global warming control schemes. How would it do that? Dump toxic waste to get back at America? But that would cause lasting damage to not only America and Denmark but to the global environment itself ... precisely what they were trying to avoid!

Unlike 'tit-for-tat' of laboratory repeated Prisoner's Dilemma, in the real world global warming game, it would be hard to limit the punishment so that it would send a strong enough signal to cooperate but not so strong as to be destructive to everyone involved.

Back to the drawing board, I guess, for utilizing Game Theory for negotiating global warming treaties.

Northern Rock and Betting on Storms

I apologize to regular readers of this blog for not updating for a while. The reason why I haven't updated is that I recently moved to the UK. I've been busy settling in so I haven't had time to update the blog.

The last couple of blogs I wrote were regarding the 'credit crunch' that was unfolding in America (where I just left a few weeks ago). It seems like trouble has followed me across the Atlantic, because Northern Rock -- a British mortgage bank -- has basically suffered a run on it in the last few days. The 'queue' (or, as we Americans call it, a line) outside the local branch of Northern Rock (it was actually more like a scrum) of depositors trying to pull their money out of Northern Rock reminded me of photos of similar scenes during the Great Depression. The BBC has adequate coverage of the situation.

As I've written before, so-called 'expert' commentators are missing the point about the 'credit crunch': The heart of the matter is that there are a bunch of credit derivatives contracts out there that are still toxic right now. I fail to see how even a large drop in rates by the Fed or the Bank of England priming the monetary pumps will solve the problem of derivatives run amok.

Speaking of derivatives and storms, Michael Lewis wrote an article for the New York Times Magazine a few weeks ago that talks about quants trading in catastrophe bonds: In Nature’s Casino (Aug. 26, 2007). You may recall I had a blog post about catastrophe bonds a while back. Michael Lewis is a great writer and I thought his article was very interesting and stimulating. Frankly, though, I wish John Seo would have stuck with math (or 'maths' in British English) rather than getting involved with derivatives trading. The article has a great quote from Dr. Seo's father when he chewed out his son for leaving academic science for Wall Street by saying, "The devil has come to you as a prostitute and has asked you to lie down with her." Apparently the senior Seo has Wall Street experience!